The trampoline jump bed can benefit from using a cover. The permatron nylon jump bed is especially easily damaged by any sparks. This is the major cause of damage - from bonfire sparks or a firework. replacement beds are expensive and will take an hour of your time to fix.
However generally, we don't use covers on our trampolines - even in winter. We want our children to be able to access the trampoline easily and get the most exercise. However it is worth having a cover for security ie if putting the trampoline 'out of bounds' or going away on holiday, and especially if having a bonfire or on firework night. Bouncy Happy people offer a wide range of trampoline covers at all prices and quality for all sizes and that can be fitted with safety nets.